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NASA NTRS1990

Computational results for flows over 2-D ramp and 3-D obstacle with an upwind Navier-Stokes solver

An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spacially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.

Venkatapathy, Ethiraj↗

NASA NTRS1990

Local sensory control of a dexterous end effector

A numerical scheme was developed to solve the inverse kinematics for a user-defined manipulator. The scheme was based on a nonlinear least-squares technique which determines the joint variables by minimizing the difference between the target end effector pose and the actual end effector pose. The scheme was adapted to a dexterous hand in which the joints are either prismatic or revolute and the fingers are considered open kinematic chains. Feasible solutions were obtained using a three-fingered dexterous hand. An algorithm to estimate the position and orientation of a pre-grasped object was also developed. The algorithm was based on triangulation using an ideal sensor and a spherical object model. By choosing the object to be a sphere, only the position of the object frame was important. Based on these simplifications, a minimum of three sensors are needed to find the position of a sphere. A two dimensional example to determine the position of a circle coordinate frame using a two-fingered dexterous hand was presented.

Pinto, Victor H.↗

NASA NTRS1990

Panel methods: An introduction

Panel methods are numerical schemes for solving (the Prandtl-Glauert equation) for linear, inviscid, irrotational flow about aircraft flying at subsonic or supersonic speeds. The tools at the panel-method user's disposal are (1) surface panels of source-doublet-vorticity distributions that can represent nearly arbitrary geometry, and (2) extremely versatile boundary condition capabilities that can frequently be used for creative modeling. Panel-method capabilities and limitations, basic concepts common to all panel-method codes, different choices that were made in the implementation of these concepts into working computer programs, and various modeling techniques involving boundary conditions, jump properties, and trailing wakes are discussed. An approach for extending the method to nonlinear transonic flow is also presented. Three appendices supplement the main test. In appendix 1, additional detail is provided on how the basic concepts are implemented into a specific computer program (PANAIR). In appendix 2, it is shown how to evaluate analytically the fundamental surface integral that arises in the expressions for influence-coefficients, and evaluate its jump property. In appendix 3, a simple example is used to illustrate the so-called finite part of the improper integrals.

Erickson, Larry L.↗

NASA NTRS1991

A critical comparison of two-equation turbulence models

Several two-equation models were proposed and tested against benchmark flows by various researchers. For each study, different numerical methods or codes were used to obtain the results which were reported to be an improvement over other models. However, these comparisons may be overshadowed by the different numerical schemes used to obtain the results. With this in mind, several existing two-equation turbulence models, including k-epsilon, k-tau, k-omega, and q-omega models, are implemented into a common flow solver code for near wall turbulent flows. The quality of each model is based on several criteria, including robustness and accuracy of predicting the turbulent quantities.

Lang, N. J.↗

NASA NTRS1990

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case.

Wu, S. T.↗

NASA NTRS1990

Numerical simulation of spatially-evolving instability

A computational study of the spatial stability of plane Poiseuille flow is presented. The numerical scheme employs a time-splitting method to integrate the full Navier-Stokes equations using spectral collocation/finite-difference discretization on a non-staggered mesh. The eigenvalue decomposition procedure is applied for the solution of the Poisson equations using the capacitance matrix technique. The buffer domain method is incorporated for the outflow boundary conditions. The input perturbation velocities are obtained by solving the Orr-Sommerfeld equation for the nonlinear eigenvalue problem employing the companion matrix method. Computational results are compared with the linear theory for two-dimensional disturbances.

Danabasoglu, G.↗

NASA NTRS1991

Numerical simulation of the reactive flow in advanced (HSR) combustors using KIVA-2

Recent work has been done with the goal of establishing ultralow emission aircraft gas turbine combustors. A significant portion of the effort is the development of three dimensional computational combustor models. The KIVA-II computer code which is based on the Implicit Continuous Eulerian Difference mesh Arbitrary Lagrangian Eulerian (ICED-ALE) numerical scheme is one of the codes selected by NASA to achieve these goals. This report involves a simulation of jet injection through slanted slots within the Rich burn/Quick quench/Lean burn (RQL) baseline experimental rig. The RQL combustor distinguishes three regions of combustion. This work specifically focuses on modeling the quick quench mixer region in which secondary injection air is introduced radially through 12 equally spaced slots around the mixer circumference. Steady state solutions are achieved with modifications to the KIVA-II program. Work currently underway will evaluate thermal mixing as a function of injection air velocity and angle of inclination of the slots.

Winowich, Nicholas S.↗

NASA NTRS1992

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

Barth, Timothy J.↗

NASA NTRS1992

Direct numerical simulation of a combusting droplet with convection

The evaporation and combustion of a single droplet under forced and natural convection was studied numerically from first principles using a numerical scheme that solves the time-dependent multiphase and multispecies Navier-Stokes equations and tracks the sharp gas-liquid interface cutting across an arbitrary Eulerian grid. The flow fields both inside and outside of the droplet are resolved in a unified fashion. Additional governing equations model the interphase mass, energy, and momentum exchange. Test cases involving iso-octane, n-hexane, and n-propanol droplets show reasonable comparison rate, and flame stand-off distance. The partially validated code is, thus, readied to be applied to more demanding droplet combustion situations where substantial drop deformation render classical models inadequate.

Liang, Pak-Yan↗

NASA NTRS1992

Development of a CFD code for internal flows in liquid fueled engines

To support the design efforts of engines in which liquid propellants are used, one is often required to analyze incompressible, two-dimensional or axisymmetric flows within ducts and cavities with rotating walls and complicated geometries. The steady-state solution is of interest in most cases. This code is intended to provide a tool for efficient computational fluid dynamics (CFD) analysis of such flow problems, taking advantage of the artificial compressibility concept and the Beam-Warming numerical scheme modified for second order accurate, implicit boundary conditions. These concepts ensure a stable, robust, and accurate algorithm due to the reduced speed of sound and the accuracy of the boundary conditions. The code is dedicated only to two-dimensional or axisymmetric flows with or without swirl. Three-dimensional computation is excluded to increase efficiency and speed. This paper briefly presents the theory of the code, as well as several benchmark applications with comparison to well known analytical solutions. In all these test cases, the code produced accurate results.

Dakhoul, Youssef↗

NASA NTRS1992

Convergence acceleration of the Proteus computer code with multigrid methods

Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.

Demuren, A. O.↗

NASA NTRS1991

A semi-elliptic analysis for 2-D viscous flows through cascade configurations

A semielliptic formulation, termed the interacting parabolized Navier-Stokes (IPNS) formulation, is developed for the analysis of a class of subsonic viscous flows for which streamwise diffusion is negligible but which are significantly influenced by upstream interactions. A two-step alternating-direction-explicit numerical scheme is developed to solve the resulting governing equations efficiently. The quasi-linearization and discretization of the equations are carefully examined so that no artificial viscosity is added externally to the scheme. Various simple channel and cascade flow configurations are examined for several values of Re, thickness ratio and Mach number, in order to establish the applicability of the IPNS model for these flows. With this model, solutions to compressible as well as nearly incompressible flows are obtained without any modification either in the analysis or in the solution procedure.

Ramamurti, R.↗

NASA NTRS1992

Aerodynamics of loaded cascades in subsonic flows subject to unsteady three-dimensional vortical disturbances

A highly efficient numerical method is developed for three-dimensional, periodic, vortical flows around a cascade of loaded airfoils. The method linearizes Euler's equations about the mean flow of the cascade and thus fully accounts for the effects of distortion of the vortical disturbances as they propogate and interact with the cascade mean flow. The numerical scheme is based on splitting the unsteady velocity into vortical and potential parts. The latter is governed by a non-constant coefficient inhomogeneous convective wave equation. A new and computationally suitable out-flow conditions are derived and avoid the difficulties associated with the singular velocity downstream. Solutions were obtained in the frequency domain by using a body-fitted coordinate system. Results are presented to demonstrate the effects of the out-flow boundary conditions, cascade spacing, mean blade loading and gust upstream conditions on the aerodynamics response and unsteady pressure field of a cascade.

Fang, J.↗

NASA NTRS1992

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

The gravitational collapse and fragmentation of centrally condensed molecular cloud cores are investigated using a new hydrodynamical code. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a 3D Cartesian grid. Two initial power-law density profiles, rho varies as r exp -1 and rho varies as r exp -2, are considered, as well as two initial density perturbations in the azimuthal coordinate theta, rho-i - rho(1 + a cos 2theta) where a = 0.1 and 0.5. Fragmentation is found to be possible in these centrally condensed cores if the initial conditions also include differential rotation. Models which collapse with initial uniform rotation do not produce fragments. If molecular cloud cores are indeed centrally condensed, as suggested by observations of star-forming regions and by studies of ambipolar diffusion, then differential rotation may be a mechanism for producing binary protostars during gravitational collapse.

Myhill, Elizabeth A.↗

NASA NTRS1992

Convection in superposed fluid and porous layers

Thermal convection due to heating from below in a porous layer underlying a fluid layer has been analyzed using the Navier-Stokes equations for the fluid layers and the extended Darcy equation (including Brinkman and Forchheimer terms) for the porous layer. The flow is assumed to be two-dimensional and periodic in the horizontal direction. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios of 0, 0.1, 0.2, 0.5, and 1.0, where this ratio is defined as the ratio of the thickness of the fluid layer to that of the porous layer. For the depth ratio of 0.1, the convection is dominated by the porous layer, similar to the situation at onset, even though the Rayleigh number for the fluid layer is well into the supercritical regime.

Chen, Falin↗

NASA NTRS1992

On the numerical treatment of nonlinear source terms in reaction-convection equations

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

Lafon, A.↗

NASA NTRS1992

Unsteady airfoil flow solutions on moving zonal grids

Euler and Navier-Stokes solutions for airfoil flows on zonal grids are presented. The governing equations are solved with an implicit, iterative, factorized numerical scheme. The inviscid fluxes are examined with a third-order accurate upwind method. Zonal grid solutions are compared with experimental measurements for flows over airfoils at fixed angles of incidence. The computed unsteady solutions for rapidly pitching and oscillating airfoils are in good agreement with experiments.

Cricelli, Antonio S.↗

NASA NTRS1992

An implicit Navier-Stokes code for turbulent flow modeling

This paper presents a numerical approach to calculating turbulent flows employing advanced turbulence models. The main features include a line-by-line Gauss-Seidel algorithm using Roe's approximate Riemann solver, TVD numerical schemes, implicit boundary conditions and a decoupled turbulence-model solver. Based on the problems tested so far, the method has consistently demonstrated its ability in offering accuracy, boundedness and a fast rate of convergence to steady-state solution.

Huang, P. G.↗